Kobe Bryant Scores Vs His Victory Contributions to team
Ge Chen
Feb.24th, 2015
RPI
Finanl Report
1.Data
Data Selection
Kobe Bryant is a famous NBA active athlete at present.Moreover, his career points made ranked in third place among all of the NBA players in the history.The dataset of Kobe historical data collected from www.basketball-reference.com, containing the modified every game data (standardlized to 36 min). The timeline of the data is between 2005 and 2007. Because :
- Kobe was the only super star in the team, other players are either rookie or role player.
- Kobe had unlimited field goals attempts.
- Kobe is at his peak (healthy and superiorly skilled)
This research is going to check whether his scoring ability will help the team toward victory or we can define it as socre to victory efficiency.
Data Summary
G:the game number Opp:opponents FG:field goal
FGA:Field Goal attempts
FGRatio:field goal percentage
ORB:offense oebound
DRB:defensive rebound
TRB:total rebound
AST:assist
STL:steal
BLK:block
TOV:turnover PF:personal fouls
PTS:scores
PLus_Minus:Victory Contribution(When Kobe is on court the team will get more goals than opponents or get less goals)
Kobe<-read.csv("~/Desktop/Kobe.csv")
head(Kobe,n=14L)## G Date Opp FG FGA FGRatio ORB DRB TRB AST STL BLK TOV PF PTS
## 1 1 11/2/05 DEN 13 28 0.464 0 5 5 4 1 2 6 4 33
## 2 2 11/3/05 PHO 13 26 0.500 2 5 7 5 0 0 3 3 39
## 3 3 11/6/05 DEN 16 31 0.516 3 5 8 5 0 1 4 2 37
## 4 4 11/8/05 ATL 15 26 0.577 1 2 3 5 1 1 1 5 37
## 5 5 11/9/05 MIN 12 26 0.462 1 3 4 4 1 0 3 0 28
## 6 6 11/11/05 PHI 7 27 0.259 3 6 9 7 1 0 3 4 17
## 7 7 11/14/05 MEM 7 18 0.389 0 3 3 2 0 1 4 3 18
## 8 8 11/16/05 NYK 15 36 0.417 3 2 5 3 2 1 0 3 42
## 9 9 11/18/05 LAC 12 35 0.343 1 3 4 5 0 0 2 2 36
## 10 10 11/20/05 CHI 17 34 0.500 1 5 6 3 2 0 3 3 43
## 11 11 11/24/05 SEA 12 26 0.462 1 1 2 5 0 0 2 4 34
## 12 12 11/27/05 NJN 14 36 0.389 0 3 3 3 2 0 5 5 46
## 13 13 11/29/05 SAS 9 33 0.273 1 3 4 0 4 1 3 0 25
## 14 14 12/1/05 UTA 11 31 0.355 2 5 7 3 2 0 2 6 30
## Plus_Minus
## 1 6
## 2 4
## 3 24
## 4 12
## 5 -11
## 6 -2
## 7 -27
## 8 6
## 9 -3
## 10 -5
## 11 15
## 12 -10
## 13 -7
## 14 1In 157 matches, Kobe can achieve 33.52 points in average, whcih is astonishing. The average victory contribution is 2.688, unveiled that when Kobe is on court, Lakers will win its opponent 2.688 point in average.
summary(Kobe)## G Date Opp FG FGA
## Min. : 1 1/10/07: 1 LAC : 8 Min. : 2.00 Min. : 7.00
## 1st Qu.: 40 1/11/06: 1 MEM : 8 1st Qu.: 9.00 1st Qu.:20.00
## Median : 79 1/12/06: 1 MIN : 8 Median :11.00 Median :25.00
## Mean : 79 1/12/07: 1 SAC : 8 Mean :11.41 Mean :25.03
## 3rd Qu.:118 1/14/06: 1 DAL : 7 3rd Qu.:14.00 3rd Qu.:29.00
## Max. :157 1/15/07: 1 DEN : 7 Max. :28.00 Max. :46.00
## (Other):151 (Other):111
## FGRatio ORB DRB TRB
## Min. :0.2220 Min. :0.0000 Min. : 1.000 Min. : 1.000
## 1st Qu.:0.3820 1st Qu.:0.0000 1st Qu.: 3.000 1st Qu.: 4.000
## Median :0.4550 Median :1.0000 Median : 5.000 Median : 5.000
## Mean :0.4565 Mean :0.9299 Mean : 4.573 Mean : 5.503
## 3rd Qu.:0.5240 3rd Qu.:2.0000 3rd Qu.: 6.000 3rd Qu.: 7.000
## Max. :0.7310 Max. :4.0000 Max. :10.000 Max. :13.000
##
## AST STL BLK TOV
## Min. : 0.000 Min. :0.000 Min. :0.0000 Min. :0.000
## 1st Qu.: 3.000 1st Qu.:1.000 1st Qu.:0.0000 1st Qu.:2.000
## Median : 5.000 Median :1.000 Median :0.0000 Median :3.000
## Mean : 4.924 Mean :1.643 Mean :0.4204 Mean :3.217
## 3rd Qu.: 6.000 3rd Qu.:2.000 3rd Qu.:1.0000 3rd Qu.:4.000
## Max. :13.000 Max. :7.000 Max. :3.0000 Max. :9.000
##
## PF PTS Plus_Minus
## Min. :0.00 Min. : 8.00 Min. :-27.000
## 1st Qu.:2.00 1st Qu.:25.00 1st Qu.: -6.000
## Median :3.00 Median :33.00 Median : 2.000
## Mean :2.79 Mean :33.52 Mean : 2.688
## 3rd Qu.:4.00 3rd Qu.:40.00 3rd Qu.: 12.000
## Max. :6.00 Max. :81.00 Max. : 35.000
## 2.Model
This research regresses the Kobe scores(PTS) per game on his contribution to victory.
attach(Kobe)
model<-lm( Kobe$Plus_Minus ~ Kobe$PTS)3.Plot
The plot is distributed around Points(20~60) and contribution[-20~20].But some outliers may arise the interst of readers. there are two matches that Kobe socred lower than 20 points, but bring a over 10 points positive contribution to the team victory.But after adding a zero line(no contribution) in the graph, we can clearly find that, in plenty of matches, even though he can score a lot, the real contribution of him to victory is negtive. In other words, when Kobe is on court, team’s total performance is worse.
plot(Kobe$PTS,Kobe$Plus_Minus, xlab="Scores(points)",ylab="Victory Contributions(points)",pch=12, cex=0.5,bg='green', main="Kobe Bryant Scores Vs. Victory Contributions")
zero<-numeric(dim(Kobe)[1])
lines(Kobe$PTS, zero, lty=2)
4.PLot with Regression Line
The regression line’s trending is upward. Kobe’s scores can help team to beat the opponents.
plot(Kobe$PTS,Kobe$Plus_Minus, xlab="Scores(points)",ylab="Victory Contribution(points)",pch=12, cex=0.5,bg='green', main="Kobe Bryant Scores Vs. Victory Contributions")
abline(model$coef, lwd=2)
5.Prediction and Confidence Interval
The research sets up a null hypothesis for Coefficeint b1 that Kobe’s score has no contribution to the team’s victory-Hbeta0:b1=0 and the alternative hypothesis Hbeta1a:b1!=0 is Kobe’s score has contribution to the team’s victory.Also, we have to set up a null hypothesis for the intercept Hbeta0:b0 =0 that Kobe has no contribution to the team’s victory when he does not score. The alternative hypothesis is that Kobe does have contribution to team’s victory(positive or negtive) when he does not score. The plot below shows the coefficents in 95% confidence interval of Kobe scores and victory contribution.We simply explain the upper bound and lower bound that 97.5% Kobe scores to victory efficiencies are no good than the efficiency in upper bound prediction and 2.5% of efficiencies are worse than the lower bound prediction. Some outliers we need to pay attention.three points exceed the predictions bound, which means that Kobe scores to victory efficiencies are unexpected high or low.
fit <- predict(model,Kobe,interval="predict",level = 0.95)
plot(Kobe$PTS,Kobe$Plus_Minus, xlab="Scores(points)",ylab="Victory Contribution(points)",pch=12, cex=0.5,bg='green', main="Kobe Bryant Scores Vs. Victory Contributions")
abline(model$coef, lwd=2)
lines(Kobe$PTS,fit[,2],lty=2)
lines(Kobe$PTS,fit[,3],lty=2)
6.Interpretation
In 95% significant level, the coefficient for Kobe’s score to his contribution to teams victory is 0.08484.Every points he made, will contribute 0.08484 points to the team’s victory.Also, when he chooses not to score,the team will be blow out by nearly 8 points. The p-value for coefficients (b1 and b0) are both significant in the level of 95%. Both null hypotheises for bo and b1 are rejected in the significant level of 95%. Therefore, Kobe does have contribution to team’s victory, when he tries to make points. The R and R-adjust square is 0.079 and 0.073 separatell, indicating that solely using independent variable-points does not well explain Kobe’s contribution to team’s victory. A better model should be implemented, by adding other independent variables such as assist, rebound, block or even the variables do not appear is this dataset, such as the average points Kobe’s matchup made , average points team made per Kobe’s pass and time length Kobe possess the ball.
summary(model)##
## Call:
## lm(formula = Kobe$Plus_Minus ~ Kobe$PTS)
##
## Residuals:
## Min 1Q Median 3Q Max
## -24.8870 -9.4341 0.3776 9.3282 26.8529
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -7.68255 2.99955 -2.561 0.011385 *
## Kobe$PTS 0.30942 0.08484 3.647 0.000362 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11.96 on 155 degrees of freedom
## Multiple R-squared: 0.07902, Adjusted R-squared: 0.07308
## F-statistic: 13.3 on 1 and 155 DF, p-value: 0.000362